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Standard XII

Mathematics

One - One function

The total num...

Question

The total number of injections (one-one into mappings) from ${a_{1}, a_{2}, a_{3}, a_{4}}$ to ${b_{1}, b_{2}, b_{3}, b_{4}, b_{5}, b_{6}, b_{7}}$ is

400

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420

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800

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840

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Solution

The correct option is C $840$
Let $A = {a_{1}, a_{2}, a_{3}, a_{4}}$

$B = {b_{1}, b_{2}, b_{3}, b_{4}, b_{5}, b_{6}, b_{7}}$

$∴ n (A) = 4, n (B) = 7$

$∴$ The total number of injections $=^{7} P_{4}$

$= \frac{7!}{3!} = 7 \cdot 6 \cdot 5 \cdot 4 = 840$

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Similar questions

Let A={a1,a2,a3,a4,a5} and B={b1,b2,b3,b4,b5} where ai's and bi's are school going students . Define a relation from A to B by xRy iff y is a true friend of x . If R={(a1,b1),(a2,b2),(a3,b3),(a4,b4),(a5,b5)} . Prove that R is neither one one nor onto

Q. Suppose four distinct positive numbers

a_{1}, a_{2}, a_{3}, a_{4}

are in

G . P

. Let

b_{1} = a_{1}, b_{2} = b_{1} + a_{2}, b_{3} = b_{2} + a_{3}

and

b_{4} = b_{3} + a_{4}

.
STATEMENT-1 : The numbers

b_{1}, b_{2}, b_{3}, b_{4}

are neither in

A . P

. nor in

G . P

.
STATEMENT-2 : The numbers

b_{1}, b_{2}, b_{3}, b_{4}

are in

H . P

Q. Suppose four distinct positive number

a_{1}, a_{2}, a_{3}, a_{4}

are in G.P. Let

b_{1} = a_{1}, b_{2} = b_{1} + a_{2}, a_{3} = b_{2} + a_{3}

and

b_{4} = b_{3} + a_{4}

Statement 1 - The numbers

b_{1}, b_{2}, b_{3}, b_{4}

are neither in A.P. nor in G.P.
Statement 2 - The numaber

b_{1}, b_{2}, b_{3}, b_{4}

are in H.P.

Q. Assertion :Suppose four distinct positive numbers

a_{1}, a_{2}, a_{3}, a_{4}

are in GP. Let

b_{1} = a_{1}, b_{2} = b_{1} + a_{2}, b_{3} = b_{2} + a_{3}

and

b_{4} = b_{3} + a_{4} .

STATEMENT- 1: The numbers

b_{1}, b_{2}, b_{3}, b_{4}

are neither in AP nor in GP, and Reason: STATEMENT- 1: The numbers

b_{1}, b_{2}, b_{3}, b_{4}

are in HP.

Let A={a1,a2,a3,a4,a5} and B={b1,b2,b3,b4,} where ai's and bi's are school going students . Define a relation from A to B by xRy iff y is a true friend of x . If R={(a1,b1),(a2,b1),(a3,b3),(a4,b2},(a5,b2)} . Prove that R is neither one one nor onto

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The total number of injections (one-one into mappings) from {a1,a2,a3,a4} to {b1,b2,b3,b4,b5,b6,b7} is

The correct option is C 840Let A={a1,a2,a3,a4}B={b1,b2,b3,b4,b5,b6,b7}∴n(A)=4,n(B)=7∴ The total number of injections = 7P4=7!3!=7⋅6⋅5⋅4=840

The total number of injections (one-one into mappings) from ${a_{1}, a_{2}, a_{3}, a_{4}}$ to ${b_{1}, b_{2}, b_{3}, b_{4}, b_{5}, b_{6}, b_{7}}$ is

The correct option is C $840$
Let $A = {a_{1}, a_{2}, a_{3}, a_{4}}$

$B = {b_{1}, b_{2}, b_{3}, b_{4}, b_{5}, b_{6}, b_{7}}$

$∴ n (A) = 4, n (B) = 7$

$∴$ The total number of injections $=^{7} P_{4}$

$= \frac{7!}{3!} = 7 \cdot 6 \cdot 5 \cdot 4 = 840$